We explore the feasibility of ultra-high density memory based on quantum devices. Starting from overall constraints on chip area, power consumption, access speed, and noise margin, we deduce boundaries on single cell parameters such as required operating voltage and standby current. Next, the possible role of quantum devices is examined. Since the most mature quantum device, the resonant tunneling diode (RTD) can easily be integrated vertically, it naturally leads to the issue of 3D integrated memory. We propose a novel method of addressing vertically integrated bistable two-terminal devices, such as resonant tunneling diodes (RTD) and Esaki diodes, that avoids individual physical contacts. The new concept has been demonstrated experimentally in memory cells of field effect transistors (FET's) and stacked RTD's.